Two-Stage BER-Surrogate-Based Resource Allocation for Uplink SCMA in IoT Networks

This paper develops a reliability-oriented resource-allocation framework for a single-cell uplink sparse code multiple access (SCMA) system with fixed low-projection codebook (LPCB) constellation components. Link-level SCMA–message-passing-algorithm (MPA) samples calibrate a compact bit-error-rate (BER) surrogate, enabling repeated candidate evaluation without embedding MPA decoding in the search loop. The proposed two-stage method combines a subcarrier allocation whale optimization algorithm (SAWOA), equipped with stochastic binary mapping and exact degree-feasibility repair, with an exact Karush–Kuhn–Tucker (KKT) active-set power allocator. For the J=6, K=4 setting, exact enumeration over all 210 main conditions shows that the SAWOA attains the enumerated equal-power P1 oracle objective within relative tolerance 10−10 in every case. Across 30 paired channel/optimizer blocks, each aggregating the seven power points, the SAWOA reduces the initial-gap-normalized convergence area under the curve by 47.5% relative to the Standard Binary WOA (Holm-adjusted p=1.19×10−5); its oracle-hit rate by iteration 20 is 93.3% versus 75.7%, while no significant AUC difference is detected relative to particle swarm optimization. After 100 iterations, the three population methods approach the same oracle plateau, whereas random is significantly worse at the midpoint (p=7.45×10−9). Exact KKT refinement improves every recorded SAWOA solution and reduces the equal-power surrogate by 3.64–56.27% on average across the sweep, with a maximum relative KKT residual of 1.01×10−16. A single-point direct Rayleigh SCMA–MPA check confirms the executable transfer of the selected allocation and returns the same decoded BER for the SAWOA and Standard Binary WOA; it remains a bounded transfer sanity check. The results demonstrate finite-budget stage-1 search efficiency, reliable feasible support recovery, and effective exact power refinement for the investigated quasi-static configuration.